Problem: Solve for $x$ and $y$ using elimination. ${3x-y = 5}$ ${-2x+y = -2}$
Explanation: We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Add the equations together. Notice that the terms $-y$ and $y$ cancel out. ${x = 3}$ Now that you know ${x = 3}$ , plug it back into $\thinspace {3x-y = 5}\thinspace$ to find $y$ ${3}{(3)}{ - y = 5}$ $9-y = 5$ $9{-9} - y = 5{-9}$ $-y = -4$ $\dfrac{-y}{{-1}} = \dfrac{-4}{{-1}}$ ${y = 4}$ You can also plug ${x = 3}$ into $\thinspace {-2x+y = -2}\thinspace$ and get the same answer for $y$ : ${-2}{(3)}{ + y = -2}$ ${y = 4}$